Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Cartesian coordinate system wikipedia , lookup
Trigonometric functions wikipedia , lookup
Rational trigonometry wikipedia , lookup
Event symmetry wikipedia , lookup
Line (geometry) wikipedia , lookup
Euclidean geometry wikipedia , lookup
Steinitz's theorem wikipedia , lookup
Name: ________________________________________________ Vocabulary Acute Angle: An angle of less than 90 degrees. Angle: The amount of space where two lines meet. Area: The number of square units that covers a certain space. Average: A value that lies within a range of values. Circumference: The distance around a circle. Congruent Shapes: Identical geometric shapes, usually facing in different directions. Cubic Unit: A unit with six equal sides, like a child's block. Customary System: Measures length in inches and feet capacity in cups and pints, weight in ounces and pounds and temperature in Fahrenheit. Data: Gathered information (datum-singular). Decimal: A number that includes a period called a decimal point. The digits to the right of the decimal point are a value less than one. Denominator: The bottom number in a fraction. Diameter: The length of a line that divides a circle in half. Digit: A numeral. Dividend: The number to be divided in a division problem. Divisor: The number used to divide another number. Equation: A number sentence in which the value on the left of the equal sign must equal the value on the right. Equilateral Triangle: A triangle with three equal sides. Equivalent Fractions: Fractions that name the same amount, such as ½ and 5/10. Estimating: Using an approximate number instead of an exact one. Expanded Notation: Writing out the value of each digit in a number. Fraction: A number that names part of something. Geometry: The study of lines and angles, the shapes they create and how they relate to one another. Greatest Common Factor (GCF): The largest number that will divide evenly into a set of numbers. Improper Fraction: A fraction that has a larger numerator than its denominator. Integers: Numbers above or below zero: -2, -1,0, + 1, +2, and so on. Intersecting lines: At least two straight lines that cross each other's paths. Isosceles Triangle: A triangle with two equal sides. Least Common Multiple (LCM): The lowest possible multiple any pair of numbers have in common. Line: A series of continuous points in a straight path, extending in either direction. Line Segment: A straight line extending from one exact point to another. Mean: The average of a group of numbers. Median: The number in the middle when numbers are listed in order. Metric System: Measures length in meters, capacity in liters, mass in grams and temperature in Celsius. Mixed Number: A whole number and a fraction, such as 1 ¾ . Numerator: The top number in a fraction. Obtuse Angle: An angle of more than 90 degrees. Opposite Integers: Two integers the same distance from 0 but in different directions, such as -2 and +2. Ordered Pairs: Another term used to describe pairs of integers used to locate points on a graph. Parallel lines: Lines that never get closer together or farther apart at any point. Percent: A kind of ratio that compares a number with 100. Perimeter: The distance around a shape formed by straight lines, such as a, square or triangle. Perpendicular Lines: Two lines that intersect each other at a 90-degree angle. Place Value: The position of a digit in a number. Probability: The ratio of favorable outcomes to possible outcomes in an experiment. Proportion: A statement that two ratios are equal. Quadrilateral: A shape with four sides and four angles. Quotient: The answer in a division problem. Radius: The length of a line from the center of a circle to the outside edge. Range: The difference between the highest and lowest number in a group of numbers. Ratio: A comparison of two quantities. Ray: A straight line extending in one direction from one specific point. Reciprocals: Two fractions that, when multiplied together, make 1, such as 2/7 and 7/2. Right Angle: An angle of 90 degrees. Rounding: Expressing a number to the nearest whole number, ten, thousand or other value. Scalene Triangle: A triangle with no equal sides. Similar Shapes: The same geometric shape in differing sizes. Straight Angles: An angle of 180 degrees. Symmetrical Shapes: Shapes that, when divided in halt are identical. Vertex: The point at which two lines intersect. Volume: The number of cubic units that fills a space. X Axis: The horizontal number line in a plotting graph. X Coordinate / Y Coordinate: Show where a point is on a plotting graph. Y Axis: The vertical number line in a plotting graph. Place Value Every digit in a number belongs in a certain place. Each place has a different value. This is a place value chart: We can use a place value chart to identify the value of a digit in a number. For example, if we put a 5 in the thousands place, the value is “five thousand” or “5,000”. Example: in the number 12,345.678 the value of the 7 is .07 or “seven hundredths” because it is in the hundredths place. Practice: Use the number 87,981,067.3845 to answer the following questions 1) What digit is in the tens place? _____ 2) What digit is in the millions place? ____ 3) The “units” place is also called the “ones” place. What digit is in the ones place? _____ 4) What is the value of the 3? ________________________________ 5) Create the number with the greatest value using only the digits 1, 9, 4, 0, 5 and 2. Write the number that is 100 less and 100 more than the given number. Example: 123 223 323 6) ________ 1,341 ________ 7) ________ 12,987 ________ 8) ________ 922 ________ 9) ________ 555 ________ 10) Write a number that has a 5 in the hundreds place and a 2 in the hundredths place: Rounding To get an approximate answer instead of an exact answer we can round numbers. Numbers can be rounded to various places, depending on how precise an answer needs to be. The ability to round numbers can be applied when doing mental math or quick calculations. When rounding, the digit to the right of the requested place tells us if we should round up or down. If the digit to the right is 5 or more, we round up. If the digit is 4 or less we round down. Remember the phrase “5 or more, let it soar. 4 or less, let it rest” Example: to round 485 to the nearest tens, we look at the digit to the right of the tens place, and the 5 tells us to round up to 490 (5 or more, let it soar). Estimate the following sums by rounding first, then adding. You can round to whichever place is reasonable for each problem. 1) 1,082 + 98 = ____________ + ____________ = _______________ 2) 2,612 + 4,411 = ____________ + ____________ =______________ 3) 822 + 922 = ____________ + ____________ = ______________ 4) 10,309 + 17,984 = ____________ + ____________ = _____________ Round each number to the nearest whole number (ones place). Example: 76.3 76 (76.3 is approximately 76) 5) 12.5 ________ 6) 907.99 ________ 7) 11.11 ________ 8) 12.01 ________ 9) 5,532.45 ________ 10) 12,040.87 ________ Round each number to the nearest hundred. Example: 11,584 11,600 (the 8 tells the 5 to go up to a 6) 11) 34,765 ________ 12) 109,023 ________ 13) 97 ________ 14) 1,395,721 ________ Patterns Patterns are numbers, designs, or objects that repeat in the same way. To find a pattern, look for the change happening to each number or shape, and then repeat for the following shapes. Find the pattern that is happening to the following design. Using that pattern, what would the next image be? 1) Next design: The pattern below is “add two, then times two”. Using that pattern, what would the next 3 numbers be? 2) 1, 3, 6, 8, 16, 18, 36, _____, _____, _____ Identify the patterns shown below. Using that pattern, what would the next 2 numbers be in each series? 3) 3, 5, 9, 17, 33 Pattern: ___________________ Next two numbers: __________, __________ 4) 100, 97, 94, 91, 88, 85 Pattern: ___________________ Next two numbers: __________, __________ 5) 4, 6, 10, 18, 34 Pattern: ___________________ Next two numbers: __________, __________ Order of Operations Order of Operations helps us to solve problems the same way so that we get the same answer. To remember the correct order, use the phrase “Please Excuse My Dear Aunt Sally… Let’s Rock!” P E MD* AS* *LR parenthesis () exponents multiplication or division addition or subtraction left to right (applies to multiplication/division and addition/subtraction) Example 6 x 8 – (4 + 2) + 32 6 x 8 – 6 + 32 6x8–6+9 48 – 6 + 9 42 + 9 51 Use order of operations to simplify: 1) 15 – 4 x 2 + 3 2) (3 + 9) – 7 + (10 2) 3) 7 + 8 x (5 + 3) – 1 4) 3 (5 – 2) + 36 5) (15 + 9 ) ( 8 – 2) 6) 9 + 3 x 7 – 5 Adding and Subtracting Decimals To add or subtract decimals, the most important thing to remember is to line up the decimal points! We line up the decimal points to line up the correct place values (add the tens to the tens, the hundredths to the hundredths, etc.). Then, add or subtract as you normally would. The decimal point drops straight down into the answer. Example: 14.2 – 2.97 14.20 Decimals are lined up - 2.97 11.23 Decimal lined up in answer Add the following decimal numbers 1) 4.50 + 1.3 = 2) 122.8 + 19.7 = 3) 56 + 8.76 = 4) 8.99 + 9.394 = (hint: 56 = 56.0) Subtract the following decimal numbers 5) 9.8 – 4.2 = 7) 12.8 – 3.9 = 6) 21.44 – 3.87 8) 65.09 – 32.76 = Application: 9) Alison had $12.50. She earned $8.75 babysitting. How much money does she have total? 10) Doug had a piece of rope 8.1 feet long. He cut off 1.2 feet of rope to use for a project. What is the length of his rope now? Multiplication of Whole Numbers Remember to regroup if you need to. Multiply 56 x 14 2 56 x 14 224 + 560 ← write a 0 to fill ones place 784 Absolutely NO LATICE work. Complete. 1. 64 x94 2. 46 x74 3. 22 x18 4. 30 x28 5. 89 x12 6. 7. 84 x71 8. 55 x80 9. 45 x92 10. 75 x20 74 x70 Show your work here; Complete. 49. 2 × (8 × 2 × 6) × 3 Complete. 53. We decided that before the bell sounded we should count the number of students present in the cafeteria. There were sixteen boys. There were twice as many girls. How many students were there in all? 50. 4 × (7 × 9 × 1) 12. Jose' family lives on a 17-acre farm. Carlos' family's farm is four times as big. How many acres are in Carlos' family farm? Division of Whole Numbers Divide until each digit in the dividend 27 33 893 Has been brought down. Write remainders as fraction. = 27 2/33 -66 233 - 231 2 Divide. Write remainders as simplified fractions. Show your work. 1. 2,178 18 2. 156 26 3. 4,833 27 4. 312 78 5. 1,328 83 6. 940 47 7. 176 88 8. 2,135 61 9. 2,623 43 10. 837 93 11. 770 77 12. 2,860 55 Fractions - Identify Shaded Portion Write a fraction to show how much of the shape is shaded. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. Fractions - Draw Shaded Portion Draw a picture to show the fractional representation. 1. two-tenths 2. 1 3. one-third 6 4. 3 5. 1 6. 4 8 2 5 7. three-fourths 8. six-sevenths 9. five-ninths 10. one-sixth 11. 1 12. 1 4 7 Fractions –Finding Equivalents, Add & Subtract Complete & Express all results in simplest form, compare denominators first. 1. 4 7 14 2. 3 9 4 3. 21 5 10 4. 1 6 42 5. 6 1 = 7 7 6. 5 2 = 6 6 7. 3 1 4 2 = 8 8 8. 2 1 7 2 = 3 3 9. 6 2 = 8 8 10. 3 1 = 6 6 11. 1 3 3 5 = 4 4 12. 2 1 = 3 9 15. 2 1 9 6 = 3 6 16. 19. 31 42 = 4 8 20. 13. 4 1 = 5 10 14. 17. 5 5 6 = 6 6 18. 15 3 2 5 = 6. Ordering Decimals/Plotting on Number line 5 1 3 2 = 9 9 17 5 1 7 = 16 8 4 3 12 10 = 7 7 Use the number line to help order the following 10 numbers from smallest to largest. First, place each point on the number line and label it. After all the points have been plotted on the number line, list the numbers in order from smallest to largest. 5 3 4 6 7 Multiplying Fractions/Mixed Numbers 8. 7. The local pizza parlor is giving away a pizza to anyone who can answer all of these multiplication problems. Marcos wants to win. Can you give him a helping hand to find the correct answers? Write the answers in the simplest form. 1. 1 2 x 5 3 2. 1 3 x 4 7 3. 1 3 x 2 8 4. 3 3 x 7 4 Remember: To multiply fractions, multiply the numerators, then multiply the denominators. 1 2 x =? 2 3 1 2 2 x = 2 3 6 Reduce 5. 5 1 x 9 3 6. 12 x 3 7. 42 x 1 2 8. 33 x 26 9. 12 x 23 10 4 1 x 31 5 7 5 5 2 3 4 7 4 2 2 to simplest terms. 6 2 =? 6 9. Division of Fractions Complete each division problem below. Then write the corresponding letter on the line in front of each problem. The letters will spell out a tongue twister. Try to say it quickly six times. ___S__ 3 1 ÷ = 4 2 _____ 1 2 ÷ = _____ 2 3 _____ 4 3 ÷ = _____ 5 5 _____ 2 5 ÷ = _____ 3 6 _____ 4 1 ÷ = _____ 7 2 _____ 2 2 ÷ = _____ 4 3 _____ 8 3 ÷ = _____ 10 5 _____ 3 1 ÷ = _____ 4 3 _____ 6 1 ÷ = _____ 8 3 _____ 11 2 4 2 ÷ = _____ 5 5 11. 10. 12. Range/Mean/Median/Mode Find the range. 1. 5, 7, 8, 8, 15,23 Find the mean. 7. 5, 7, 8, 8, 15, 23 2. 42, 48, 53, 54, 57,59,60,61,61 8. 42, 48, 53,54, 57, 59, 60, 61, 61 3.22,23,26,31,38,41,45,62 9. 22, 23, 26, 31, 38,41, 45, 62 Remember: Range is the difference between the greatest and the least number in a set of data. 21,15,27,12, 20 Find the median. 4.5,7,8,8,15,23 5. 42,48,53,54, 57, 59, 60,61,61 Remember: Mean is the average of a set of data. Add the numbers, and then divide the sum of the numbers by the number of addends. 21 + 15 + 27 + 12 + 20 = 95 95 ÷ 5 = 19 The mean is 19. Find the mode. 10.5, 7, 8, 8, 15, 23 6.22, 23, 26, 31, 38, 41,45,62 11.42, 48, 53, 54, 57, 59, 60, 61, 61 Remember: Median is the middle number in a set of data. Arrange the numbers from least to greatest. The middle number is the median. 12,15,20,21,27 The median is 20. 12. 22, 23, 26, 31, 38, 41, 45, 62 Remember: Mode is the number that appears the most often in a set of data. Some sets have no mode. 21,15,27,12,20 There is no mode. 23,18,6,15,6 The mode is 6. Number Lines/Mean/Median./Mode/Range Probability/Coordinate Points Fill in the circle next to the correct answer. Use this number line for numbers 1 through 4. A B C D 6. What is the probability of drawing a white marble at random from the bag? A. 1/2 B. 1/3 C. 2/11 D. 2/9 7. What is the probability of drawing a black marble at random from the bag? A. 1/2 B. 9/11 C. 3/6 D. 3/4 1. Which point is located at -2? A. point A C. point C B. point B D. point D For numbers 8 through 11, use the following data: 13. 14. Which point is located at 3? A. point A C. point C B. point B D. point D 3. Which point is located at 1? A. point A C. point C B. point B D. point D 4. Which point is located at -3.5? A. point A C. point C B. point B D. point D 8. What is the mean of the data set? A. 19 B. 30 C. 31 9. What is the range of the data set? A. 25 B. 10 C. 15 10. What is the mode of the data set? A. 29 C. both 29 and 35 B. 35 D. there is no mode 11. What is the median of the data set? A. 29 B. 30 C. 32 5. Draw a number line and number it from -3 to +3, with 0 right in the middle. Write an S on the value of -1 and a W on the VALUE OF 2. 15. For numbers 6 and 7, use this bag of marbles. 12. Plot point A at (-2, 1) and point B at (0, -2) on this graph. D. 32 D. 35 D. Graphing Methods Tables and different kinds of graphs have different purposes. Some are more helpful for certain kinds of information. The table and three graphs below all show basically the same information-the amount of money Mike and Margaret made in their lawn-mowing business over a 4-month period. 5. 6. Combined Income per Month Margaret Combined Income per Month 75 70 65 60 55 June July Aug Sept 7. Combined Income per Month Directions: Study the graphs and table. Then circle the one that answers each question below. 75 70 65 60 55 June July Aug Sept 1. Which one shows the fraction of the total income that Mike and Margaret made in August? table line graph bar graph circle graph 2. Which one compares Mike's earnings with Margaret's? table line graph bar graph circle graph 3. Which one has the most exact numbers? table line graph bar graph circle graph 4. Which one has no numbers? table line graph bar graph circle graph 8. Which two best show how Mike and Margaret's income changed from month to month? table line graph bar graph circle graph Function Tables Complete each of the following function tables using the given rule: 1. 2. 3. - Rule = +27 Input Rule = 15 Output Input Rule = +4 - 3 Output Input 1 25 4 11 19 15 16 15 23 23 13 34 4. 5. Rule = x2 + 3 Input 6. Rule = ÷2 + 1 Output Input 2 4 4 16 9 Output Input Rule = x3 - 12 Output Output 19 40 8 38 7. Input Rule = x3 - 5 13 15 Output 1 9. 8. Rule = ÷3 - 2 Input Output Rule = x5 + 1 Input Output 12 12 16 8 15 21 3 3 5 39 41 51 Measurement Fill in the answer Convert each measure to inches. 1. 3. 5. 7. 3 ft = _______ in 8 yd = _______ in 2 ft = _______ in 5 yd = _______ in 2. 4. 6. 8. 7 in 8 yd = _______ in 8 yd 1 in = _______ in 5 in 2 ft = _______ in 3 ft 2 in = _______ in Convert each measure to feet. 9. 2 ft 8 yd = _______ ft 10. 3 mi = _______ ft 11. 108 in 8 yd = _______ ft 12. 4 yd = _______ ft 13. 1 mi 10 yd = _______ ft 14. 9 yd = _______ ft Convert each measure to feet and inches 15. 39 in 3 yd = _______ ft _______ in 16. 102 in = _______ ft _______ in 17. 13 in 1 yd = _______ ft _______ in 18. 87 in = _______ ft _______ in 19. 3 mi 102 in = _______ ft _______ in 20. 85 in = _______ ft _______ in Geometry Basics These are some geometry words that you should be familiar with: ANGLES Acute angle – an angle that measures greater than 0 but less than 90 Obtuse angle – and angle that measures greater than 90 but less than 180 Straight angle – basically a straight line: measures exactly 180 Right angle – measures exactly 90 LINES Ray –has one end point, and goes on forever in the other direction Line – goes on forever in both directions Line segment – has two endpoints Practice: Identify the following angles. On the line below each angle, label each one as either “acute”, “obtuse”, “straight” or “right”. 1) 2) 3) __________ ____________ 4) 5) ________ 6) __________ _____________ ________ Identify the following images. On the line below each image, label each one as either a “ray”, “line”, or “line segment”. 7) 8) 9) ________________ _______________ __________ Lines of Symmetry A line of symmetry is a straight line drawn through a shape that creates mirror images on both sides. If you fold the shape in half on the line of symmetry, both sides will match up perfectly. Shapes can have no lines of symmetry, one line of symmetry, or many lines of symmetry. Line of symmetry In this pentagon, there is one line of symmetry. This line cuts the shape in half so each side is a mirror image of the other side Draw as many lines of symmetry as you can in the following shapes. Below each shape, write how many lines of symmetry you were able to find. If there are no lines of symmetry, write “none” 1) 2) __________ 3) ___________ 4) _________ 5) __________ 6) ______________ ____________ Graphing Coordinate Points To graph coordinate points, remember the phrase “run before you jump”. Each coordinate point is made up of an X coordinate and a Y coordinate. X is horizontal (left to right) and Y is vertical (up and down). Run left or right to the X coordinate, then jump or fall to the Y coordinate. Example: plot the point (-2, 3) This means run left to –2, then jump up 3 Practice: On the coordinate plane below, plot each of the following points. As you plot each point, connect it to the previous point by using a ruler (connect the dots). When you are done connecting all points you should see a picture of a tired dog. The “start” and “stop” begin and end new lines. DOG TIRED Start (4,4) , (5,4) , (6,2) , (0,2) , (1,4) , (4,4) , (4,10) , (1,10) , (4,18) , (21,18) , (24,10) , (21,10) , (21,9) , (16,9) , (14,8) , (12,10) , (10,10) , (9,9) , (9,7) , (6,5) , (6,3) , (7,2) , (9,2) , (11,4) , (11,6) , (12,7) , (11,8) Stop Start (14,8) , (15,6) , (15,4) , (14,3) , (11,3) , (10,2) , (17,2) , (17,3) , (16,4) Stop Start (20,6) , (20,5) , (22,3) , (20,3) , (19,4) , (18,3) , (18,2) , (24,2) , (25,3) , (25,6) , (23,8) , (21,9) Stop Start (11,4) , (12,3) Stop Start (9,7) , (10,7) Stop y 10 8 6 4 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 x